Question
Can I practice Krsna consciousness if I am in a monogamous homosexual relationship?
Answer

There are many ISKCON devotees with a homosexual orientation. Many years ago, ISKCON did not have such an enlightened view on the matter, but today most devotees, including leaders, are simply happy to see a person taking to Krishna consciousness.
My view is that one’s sexuality is a private matter, and really no one else’s business. By practicing Krishna consciousness, we gradually understand that we are not the material body. All of us are equally pure souls, and so our bodily orientation is simply an external covering of the pure soul.
The same rules apply for everyone. Whatever one’s orientation, we all try to help and encourage each other to transcend the false bodily identity and learn to love Krishna.
Regarding relationships, I have been insisting for many years that monogamy is much better than promiscuity, regardless of orientation. So, devotees in faithful, monogamous relationships are all on the same level, and have the same opportunity, with the same rules, to advance in Krishna consciousness. Most ISKCON centers will welcome you. There are probably still some medieval pockets here and there in ISKCON, but they are rapidly disappearing and the majority view is one of respect for anyone who is doing their best to advance in Krishna consciousness.
Monogamy is always better than promiscuity. Prabhupada said that Krishna consciousness is a gradual process, and we see practically that most devotees cannot practice lifelong celibacy. Therefore for most devotees, gradual detachment practiced within a Krishna conscious marriage is the norm. In fact, society has a vital rational interest in encouraging all non-celibates to be monogamous, and not promiscuous, to avoid degrading society. Since Vaishnava Shastra does not speak about homosexuality, there is no rule either approving or forbidding gay marriage. There is also no injunction in Shastra that “marriage must be between a man and a woman.” My impression is that Shastra tends to be pragmatic, and ‘real world.’
Now, I will explain what I consider to be the real problem: shameless public displays of sexuality. Sexual intercourse, as Krishna explains, is pious when performed in strict conformity with Dharma. The idea of being ‘proud’ of one’s lust is absurd ignorance. We find that the heterosexuals have shamelessly sexualized public life, media etc. So the gays, wanting to be ‘equal’ in a society obsessed with equality, declare their pride in their lust, which is just as stupid as pride in hetereo-lust.
The real solution is Krishna consciousness, modesty, spiritual standards etc.